Question: Solve for $x$ : $2x^2 - 30x + 108 = 0$
Solution: Dividing both sides by $2$ gives: $ x^2 {-15}x + {54} = 0 $ The coefficient on the $x$ term is $-15$ and the constant term is $54$ , so we need to find two numbers that add up to $-15$ and multiply to $54$ The two numbers $-6$ and $-9$ satisfy both conditions: $ {-6} + {-9} = {-15} $ $ {-6} \times {-9} = {54} $ $(x {-6}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x -9) = 0$ $x - 6 = 0$ or $x - 9 = 0$ Thus, $x = 6$ and $x = 9$ are the solutions.